On the Lyapunov Matrix of Linear Delay Difference Equations in Continuous Time [PDF]
, 2016 The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the case of single
E. Rocha, Sabine Mondi'e, M. Di Loreto
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ON Ψ-INSTABILITY OF NON-LINEAR MATRIX LYAPUNOV SYSTEMS
Demonstratio Mathematica, 2009 AbstractWe prove necessary and sufficient conditions for Ψ-instability of trivial solutions of linear matrix Lyapunov systems and also sufficient conditions for Ψ-instability of trivial solutions of non-linear matrix Lyapunov systems.
Murty, M. S. N. +3 more
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Numerical solutions to large-scale differential Lyapunov matrix equations [PDF]
Numerical Algorithms, 2017 In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations.
M. Hached, K. Jbilou
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A Lyapunov functional for a system with both lumped and distributed delay
Archives of Control Sciences, 2017 In the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix.
Duda Jozef
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Multi‐parametric iterative algorithms for discrete periodic Lyapunov matrix equations
IET Control Theory & Applications, 2020 Two multi-parametric iterative algorithms are developed to solve the forward discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic systems.
Ai-Guo Wu, Wen-Xue Zhang, Ying Zhang
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Solution of Positive Periodic Discrete Lyapunov Equations with Applications to the Balancing of Periodic Systems. [PDF]
, 1997 The discrete-time positive periodic Lyapunov equations have important applications in the balancing and potentially also in the model reduction of discrete-time periodic systems.
A. Varga, Varga, A., Andreas Varga
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Construction of an iterative method for solving a class of complex symmetric generalized Lyapunov matrix equation and application to Helmholtz equation [PDF]
AUT Journal of Mathematics and ComputingThe Lyapunov matrix equations occur in many branches of control theory, such as stability analysis and optimal control. In this work, we introduce a novel iterative approach to address the generalized Lyapunov matrix equation within the framework of ...
Akbar Shirilord, Mehdi Dehghan
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State Estimation for Standard Neural Network Models with Time-Varying Delays
Complexity, 2022 The paper deals with the issue of state estimation for standard neural network models with time-varying delays. A new augmented vector with the derivative of the state is introduced in the Lyapunov–Krasovskii functional. The state estimation criteria are
Jin Zhu, Tai-Fang Li, Huanqing Wang
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Determining the domain of attraction of hybrid non-linear systems using maximal Lyapunov functions [PDF]
, 2010 summary:In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions $V_n$ in a rational functional ...
Hangos, Katalin M. +3 more
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Bound on Lyapunov exponent in $$c=1$$ c=1 matrix model
European Physical Journal C: Particles and Fields, 2020 Classical particle motions in an inverse harmonic potential show the exponential sensitivity to initial conditions, where the Lyapunov exponent $$\lambda _L$$ λL is uniquely fixed by the shape of the potential. Hence, if we naively apply the bound on the
Takeshi Morita
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